I don't wish to split the hairs too close between preacher and evangelist. The differences between them are minuscule in my mind. That is not to say that I don't believe there are not differences. Preaching was meant for edification of the believer.
I see evangelism as for the unbeliever.
You don't need to zealeously preach before believers (although, quite frankly we could use some of that). You do need to give moral instruction. This also shouldn't be confused with teaching.
I see all three of these as different roles. Can a great preacher be a great evangelist or visa versa. Absolutely-many have been. That doesn't mean worship service was meant to evangelize.
I could counter your sarcasm by saying perhaps your church is so busy evangelizing 24/7 that it does not take the time out to worship God in the beauty of His holiness. Much like Martha running around while Mary sat at our Lord Jesus' feet. But I won't. ;O)
Enough said on this topic.
If you are going to preach the gospel, you are going to reap the harvest. The more people you preach the gospel to, the more people are going to be harvested. Jesus said the harvest is plenty but the laborers are few. So those that are willing to do the labor in harvesting (i.e., preaching the gospel TO THE LOST) are going to experience the most harvesting of lost souls.
I would be willing to bet that your Church is engaged in active evangelism from the pulpit. You probably don't like it, but the church you have chosen is probably one of the ones who believes that the church is not only a place to equip the saints, but also a place in which to reap the harvest.
If you do not do evangelism under the roof of your church, then how do YOU do it? Do you go out into the streets every day and preach the gospel from the street corners? Or do you leave that job up to those who have been called to be street preachers.